What would be an example of funny or general business topics for a five minute presentation to a very diverse audience?

It is always best to determine your speech topic based on your audience.  If you have a very general audience, try to match your topic to the occasion instead.  For example, if the audience is mixed but it is a graduation, then you base your speech on celebrating accomplishment, moving on, or success.  These are typical graduation topics. 
Making a humorous speech can be a big hit.  However, you will want to plan carefully.  Make sure that your jokes are tasteful and not at anyone’s expense.  Do not try to be funny by making fun of someone else, in other words.  This could backfire.  When trying to be funny with a wide audience, you have to be very careful.  Make sure you are not being bitter or vicious. 
The best way to make a speech appeal to a wide audience is to plan it around a theme that will appeal to the widest number of people, and then inject some humor where possible.  In other words, rather than trying to plan a comedy routine, write a meaningful speech and include some jokes.
http://teacher.scholastic.com/writewit/speech/tips.htm

Explain five differences between a solstice and an equinox.

One difference is the amount of daylight that a particular place on the globe is going to experience. You may have noticed that "equinox" is similar to the word "equal." That is a good connection to make because an equinox represents a day (March 20 or 21 and September 22 or 23) when the duration of day and night are equal. A solstice, on the other hand, represents a time when the day is longest (June 21) or a time when the day is shortest (December 21). This does not mean the 24 hour day/night cycle has changed. It just means that the number of daylight hours is at the maximum or minimum. This is because Earth's rotational axis is tilted, and Earth revolves around the sun. At the summer solstice, Earth's geographic north pole is tilted toward the sun. Therefore, there are more sunlight hours than dark hours. The winter solstice sees the north pole pointing away from the sun, so daylight hours are shorter. The spring and fall equinoxes are times when the northern and southern hemispheres receive equal amounts of sunlight. The sun is directly "above" the equator. The equinoxes coincide with spring and fall, and the solstices coincide with winter and summer. Finally, the days shorten or lengthen following the equinoxes, but the solstices are the shortest or longest days: after them, the daylight length will reverse. The days get shorter as we approach the fall equinox and the winter solstice, and the days get longer as we approach the spring equinox and summer solstice. Then, the entire process will reverse.
https://localtvwhnt.files.wordpress.com/2016/09/autumnal-equinox-explainer.png

https://multifiles.pressherald.com/uploads/sites/4/2017/09/autumnal-equinox-sf.jpg

After reading her diary until chapter 1, what impression can we make about Anne?

Questions asking for subjective answers are based upon a personal understanding and "relationship" with a text and character. Subjective answers will differ from one reader to the next. These differences between readers' perspectives lie in the fact that all readers have different points of view that they bring with them into a reading. For example, a reader's perspective can change due to gender, age, culture, society, morals, experiences, or parenting, to name a few factors. As a teacher, I tend to accept most student-presented impressions of a text, as long as there is support for why the student feels the way they do. As for a general impression that Anne makes in the opening chapter, one needs to look at a few different aspects.
First, Anne's story opens with the following line: "I hope I will be able to confide everything to you, as I have never been able to confide in anyone, and I hope you will be a great source of comfort and support." Here, Anne shows her trust in us as readers and human beings. Although she does not know us, she is willing to trust us. One can either become endeared to her or estranged. The endearment would exist because she immediately trusts us and knows nothing about us. She is unwilling to pass judgment on us. One may, on the other hand, find this immediate trust alienating. One could ask himself or herself how Anne could trust someone so immediately. He or she may believe Anne to be naive and ignorant regarding the ways of the world. This said, one must also remember that Anne's "you" is her diary and not the reader. Upon remembering or realizing this, one's initial thoughts on Anne may (should) change.
Based upon the ideas mentioned earlier about reader perspective, one may feel as though Anne is quite spoiled. She receives many presents for her birthday. A reader from an impoverished background may feel like Anne is bragging at this point. Other readers may feel like Anne does not get much, if they are richer and get more than what she describes for their own birthdays.
As Anne details her "friends" and schoolmates, she uses language that many readers may relate to. As social beings, we seek out relationships. As these relationships grow, we learn about who the people really are. Anne's detailing of these relationships shows her as a strong young girl with very specific thoughts on the people around her. All ages of readers should be able to relate to her descriptions.
One statement which may make readers feel for Anne is the following: "I don't have a friend." Given our social nature, people need friendships and relationships. The idea that Anne has no friends and is "speaking" to her journal may make many feel sorry for her (especially given that most people know the story the diary tells).
In the end, Anne comes across as an honest young girl who wants nothing more than a friend.

what does Madame loisel learn from Mme. Forestier when she runs into her on the street a decade later?

Mathilde Loisel is the protagonist in Guy de Maupassant's "The Necklace." Though she is both "pretty and charming," she does not have the wealth nor the lifestyle that she desires. Upon receiving an invitation to an important social affair, Mathilde spends money on a dress because she feels she has nothing worthy. Since she cannot afford to purchase a necklace, she borrows one from her friend, Mme. Forestier. Mathilde finds, "in a black satin case, a superb diamond necklace," which her friend easily agrees to loan her.
When Mathilde and her husband return home from the social affair, she realizes she has lost the necklace. She decides not to tell her friend but instead decides to purchase a similar necklace to give to Mme. Forestier as the original. Mathilde and her husband borrow a large sum of money, thirty-six thousand francs, to purchase a new necklace. It takes ten years to repay the debt.
After repaying the debt, Mathilde sees her friend, Mme. Forestier, and tells her the truth about the necklace. She informs Mme. Forestier that she and her husband spent ten years paying for the diamond necklace. Mme. Forestier is surprised, telling her, "But mine was imitation. It was worth at the very most five hundred francs!" Mathilde learns that she and her husband spent thirty-six thousand francs when the necklace was only worth a fraction of that amount.

What makes the narrator doubt whether he should ever come back?

When Robert Frost writes "I doubted if I should ever come back", what he's indicating is doubt that he'll ever be able to return to the position he's currently in. He's comparing his awareness within a situation where an important choice must be made to having to choose a path in the woods. He expresses the seriousness of this choice by saying that he'll likely never be able to return to this moment of power or clarity over these choices after the decision is finally made, and that future important choices will compel further action instead. Frost is illustrating powerlessness over what may happen next, and concludes the poem with a sigh and by saying that he took the path less traveled, which made all the difference. In other words, despite all the challenges there are to making an important decision, Robert Frost expresses that he chose to live a certain way in order to cope with these hardships, and that certain aspects of life are beyond the individual.

The narrator knows how "way leads on to way," and this is why he believes he will not make it back to this particular spot. In the poem, the two roads are symbolic of two choices, and, typically, when we make one decision, that leads to more choices and other decisions, and our next decision leads to new choices and more decisions. The likelihood that one would actually be able to retrace one's steps, so to speak, and somehow return to that one particular decision, having had to make so many since then, is not good. Even if it were possible, would we really want to undo or unmake all the choices we have selected? I doubt it, and so must he. That’s just the way life is.

How does the setting in "The Cask of Amontillado" change with specific examples?

As the story opens it is Carnival season in Italy. Montresor capitalizes on the fact that Fortunato has been out drinking to celebrate the season; it is rather easy in these circumstances to lure Fortunato to his palazzo on the pretext of sampling a rare cask of Amontillado wine.
The next setting is the interior of the palazzo, and Montresor escorts Fortunato to the catacombs beneath his home where the wine vaults are located. Along the way, Montresor points out nitre on the walls. The nitre is used as a foreshadowing device, due to the fact that it is an irritant which induces coughing, sneezing, and general breathing problems. The two men stop and share a bottle of Medoc where Montresor offers an ironic toast to Fortunato's "long life."
Because the vaults are extensive the men continue walking deep underground; this enables a conversation about the symbolism of the shield of the Montresors and foreshadows what Montresor will do to Fortunato. The two men pass piles of skeletal remains interspersed with "casks and puncheons" of wine.
The men's journey ends at a recess in a deep crypt. It is described as "in depth about four feet, in width three, in height six or seven." It is the perfect height for a small vertical tomb, which is what it becomes for Fortunato when Montresor successfully chains him inside and seals it.
https://www.ibiblio.org/ebooks/Poe/Amontillado.pdf

What is the significance of birth order?

There seems to be little consensus among the scientific community regarding the subject of birth order. Some experts believe that birth order merely decides personalities while others believe that birth order actually affects destinies.
That being said, firstborns are said to be achievement-oriented, methodical, and dependable. Parents are said to spend more time with their firstborns than with their other children. Also, parents depend heavily on their firstborn children to set good examples for their siblings. According to research, almost 100% of astronauts are either the firstborn children or the oldest sons of their families. Firstborns are also said to gravitate toward careers in technology, engineering, and science. Many world leaders and CEOs are firstborns, notably Thomas Jefferson, Theodore Roosevelt, Winston Churchill, Steve Ballmer (of Microsoft), and Joe Moglia (of TD Ameritrade).
Middle children are often said to be socially-astute and loyal. It is said that 80% of middle children prove to be more loyal to their spouses than 65% of firstborns and 53% of last-born children. Middle children are said to gravitate toward careers in law enforcement, public service, education, and healthcare. They are said to be the mediators and peacemakers of the sibling world. Experts say that these traits translate into who middle children become as they get older. As an example, Martin Luther was a middle child, and he worked to foster equality and understanding between white and black Americans.
The youngest children of families tend to be outgoing, sociable, attention-seeking, and fun-loving. They also tend to sympathize with the downtrodden, simply because their early childhood experiences were often accompanied by a sense of helplessness. Youngest children gravitate toward careers in sales, art, and design. A modern example of a fun-loving and outgoing personality is Prince Harry. Perhaps because his extroverted personality is combined with his sensitivity towards the downtrodden, Prince Harry is responsible for bringing to fruition the Invictus Games. The Invictus Games is an international Paralympics sports event created by Prince Harry for wounded soldiers or veterans; it made its debut in 2014 in London.
While birth order is significant, many experts argue that it is only significant in helping us to understand who we are. If we can learn to understand how birth order affects us, we can overcome certain destructive, inherent tendencies, and we can become our best selves in the process.
 
https://www.bestpsychologydegrees.com/birth-order/

https://www.psychologies.co.uk/birth-order-effect

Where do cells get the energy they need to create the energy-rich compound ATP?

There are lots of different kinds of cells that exist; therefore, describing a single method by which every cell makes ATP is not possible.  I believe that the question is likely asking about human cells.  With that in mind, the general, broad answer is that cells create ATP energy from chemical reactions that begin with glucose and oxygen. 
The process is called cellular respiration. The basic formula is as follows:
Glucose + Oxygen --> Carbon Dioxide + Water + ATP
Cellular respiration can be divided into a few main steps.  The first step is glycolysis.  It will produce a net gain of 2 ATP.  The 2nd step is respiration.  This step is also called the Kreb's Cycle.  It will produce 2 more ATP.  This is followed by the electron transport chain.  In general, it will produce a 34 ATP units, but that number can vary depending on the cell type.  That gives a total of 38 units of ATP that cells produce from glucose and oxygen through the process of cellular respiration. 
http://dvbiology.org/biologyweb/bcresp.htm

https://sciencing.com/formula-cellular-respiration-5513197.html

McDougal Littell Algebra 2, Chapter 3, 3.1, Section 3.1, Problem 75

(2, -6), (-1, 7)
To solve this, we can substitute the x and y values into the equation to see if they are solutions. First, let's substitute the (2,-6).
6(2)+0.5(-6)<=-5
12-3<=-5
9<=-5
9 is not less than or equal to -5. Therefore, (2,-6) is NOT a solution of the inequality. Now we substitute the other x and y value which are (-1,7) to check if they are solutions.
6(-1)+0.5(7)<=-5
-6+3.5<=-5
-2.5<=-5
-2.5 is not less than or equal to -5. This means that (-1,7) are also not solutions of the inequality. Therefore, both (2,-6) and (-1,7) are NOT solutions for this inequality.

What is a good introduction for the novel Animal Farm surrounding the topic of corruption of power?

There are a number of ways in which you might write an introduction for this essay. Firstly, you could explore the key words in the title and thereby establish the parameters of your discussion in the main body of the essay. For example, there are lots of different types of power in Animal Farm. There is the physical power represented by the dogs, and then there is the power of propaganda, represented by Squealer. There is also the power of ideas, represented most of all by Old Major and the speech he gives to the other animals in the opening chapter. You might choose in your essay to focus on one or two types of power, and the introduction is a good place to signal to the reader what your specific focuses will be. The other key word in the question, "corruption," broadly means the debasement of something which was good. That might encompass moral corruption, ideological corruption, or even physical corruption. Again, in your introduction, you might introduce the specific types of corruption that you will be focusing on in the main body of the essay.
A second option is to set up some of the debates that you might deal with in the main body of the essay. For example, you might touch upon the question of what type of power corrupts most or upon the question of whether power corrupts all types of people (or animals) equally or some types of people more than others. Introducing a few broad ideas about debates like these, which you can go into in more detail in the main body of the essay, is always a good way to begin.
A third option is to outline some of the contextual influences behind the book. For example, you might look at Orwell's time spent fighting for the Republican army in the Spanish civil war and trace some links between that time in Orwell's life and some of the ideas about power in the book. Alternatively, you could of course make some links between some of the people (Mussolini, Franco, Hitler, Lenin, Stalin) and organizations that exercised power in Orwell's life and the characters who exercise power in Animal Farm.
I hope one of these ideas appeals to you. Good luck with your essay!

One might begin such an introduction by stating that Animal Farm is an allegory, a representation in metaphorical terms of an actual series of historical events. The takeover of the Manor Farm is symbolic of the Bolshevik Revolution of 1917. What at the time was greeted by socialists worldwide as an epic event that would eventually transform the whole world deteriorated eventually into the cruel dictatorship of Joseph Stalin. In Orwell's story, the animal leadership start out with apparently good intentions and egalitarian ideals. The problem is that a power struggle inevitably occurs between the leaders, Napoleon and Snowball, and the former, the more ruthless of the two, wins out. In contrast to the stated ideals of the animals, Napoleon begins to control and to dominate the others, since the fact of exercising force in the first place (which was necessary in order to accomplish the Revolution) has corrupted him. It is as if a chain reaction or a self-perpetuating process has occurred in which those who wield any degree of power will seek to become still more powerful, causing the whole movement for equality to self-destruct.

Suppose a 32.6 g sample of CaSiO3 is reacted with 30.1 L of HF at 27.0 °C and 1.00 atm. Assuming the reaction goes to completion, calculate the mass (in grams) of the SiF4 and H2O produced in the reaction.

The balanced chemical equation for the reaction can be written as:
CaSiO_3 + 6HF -> SiF_4 + 3H_2O + CaF_2
 
The molar masses of the species of interest are:
CaSiO3 = 116.16 g/mol
SiF4 = 104.08 g/mol
H2O = 18 g/mol
 
Using the given data, moles of CaSiO3 = 32.6 g/ 116.16 g/mol = 0.281 moles
 
Similarly, moles of HF = PV/RT (using the gas law) 
 = (1 atm x 30.1 l)/(0.0821 l atm/mol/K x (27 + 273) K) = 1.22 moles
 
Using stoichiometry, 1 moles of CaSiO3 reacts with 6 moles of HF.
i.e., 0.281 moles of CaSiO3 will react with 6 x 0.281 moles = 1.686 moles of HF.
Since the available amount of HF is less than 1.686 moles, HF is the limiting reactant. 
 
Again using stoichiometry, 6 moles of HF produces 1 moles of SiF4.
Hence, the moles of SiF4 produced = 1/6 x 1.22 moles = 0.203 moles
and the amount of SiF4 produced = 0.203 moles x 104.08 g/moles = 21.13 g.
 
Similarly, the amount of water produced = 3/6 x 1.22 moles x 18 g/mol = 10.98 g.
 
Hope this helps.

What is the black spot in Treasure Island?

The Black Spot is enough to send veteran pirate Billy Bones into a fatal downward spiral of a alcoholism. So what is it?
The black spot is literally just that, a black spot. It consists of a round piece of paper with a blackened spot on one side and a message on the other. It represents a condemnation of one pirate by his crew. If given to a captain, it means that his crew has lost faith in his ability to lead is forcing him to step down from his command. In the case of Billy Bones, the message on his black spot is a demand that he appear before his former crew. It is presumed that failure to comply with a black spot could result in the death of the recipient.
In a way, the use of the black spot represents the democratic nature of pirate crews. Anyone can earn the censure of his shipmates and be called to task. Even captains are subject to them. Long John Silver receives a black spot that threatens to depose him. Only his cunning, manipulation, and shrewdness allows him to retain command.

The black spot is an age-old pirate tradition, though it was actually invented by Robert Louis Stevenson himself. What happens is that, when members of a pirate crew are dissatisfied with their captain, they present him with a piece of paper with a black spot printed on one side. This is a warning that the captain in question is about to be overthrown, or maybe even killed. Either way, the pirate captain who receives the black spot has been put on notice that he's in serious danger of losing his ship's command as well as his life.
As one can imagine, receiving the black spot can be a pretty scary experience. But it doesn't work with everyone, though. Long John Silver himself receives a black spot, but he's unconcerned. For one thing, his black spot has been drawn on a page crudely torn from the Bible. Pirate folklore states that that will bring bad luck to whoever it was that tore out the page.

In John Boyne's The Boy in the Striped Pajamas, how is Shmuel on a hero's quest?

The search for his father represents Shmuel's heroic quest in The Boy in the Striped Pajamas.
All heroic quests begin with an important mission.  Shmuel divulges this when he tells Bruno that he must find his father.  Shmuel tells Bruno that his father "went on work duty with some other men and none of them have come back."  Shmuel further informs Bruno that while he did "some exploration" to try to find him, he was not successful.
Like many heroic quests, Shmuel enlists help on his mission. When Bruno proposes to cross the fence into "Out-With," Shmuel recognizes that he could have assistance. Shmuel recognizes the value of having "someone to help him in the search for his papa." When Bruno crosses into "Out-With," he does not like what he sees and wants to return home.  As with many archetypal heroic voyages, the hero's focus does not deviate despite calls of protest or resistance.   When Bruno says he wants to stop looking, Shmuel reminds Bruno of the mission at hand:  "Shmuel stopped walking and starred at him.  'But Papa,' he said, 'You said you'd help me find him."  Upon being reminded of his promise and the importance of the quest, Bruno agrees and both boys continue to search until they are no longer able to do so.  
While it might not have been intentional, Shmuel sacrifices his life for the quest.  This shows a hero who gives everything they have to fulfill their quest.

How did the Roman Catholic Church control daily life in medieval Europe?

In medieval Europe, the Roman Catholic Church was the most powerful church, and its power was formidable and far-reaching. Church leaders controlled almost all aspects of medieval life, and the Church served many functions that in today's society we would consider to be governmental functions, such as law making/enforcement, military leadership, and granting ownership of land. The Church even controlled the ruling parties; for example, a King would need the Pope's permission to get a divorce.
Ultimately, the vast majority of people were concerned with getting into heaven, and so the Church's power was derived from their perceived ability to control whether or not a person made it there. People spent significant time and effort to avoid being punished for their sins in purgatory.The Church sold indulgences, which were papers that absolved you of punishment for certain sins. Many people signed up to fight in the Crusades or went on pilgrimages to earn forgiveness for their sins.
Serfs were expected to provide free labor for Church land, in addition to the 10% tithe. Because most serfs at the time lacked access to actual coinage, they paid their tithes in the form of grain or livestock.

The Church formed a vital part of most people's lives in medieval Europe. Just about everyone at that time was a Christian believer, and as the Church was the only one in Europe in the centuries leading up to the Reformation, it inevitably exercised considerable control, both spiritually and temporally. For the Church wasn't simply a spiritual body; it was a major temporal power in its own right with substantial wealth and property, mainly in the form of extensive landholding. This gave the Church considerable leverage over the crowned heads of Europe. If any of these rulers acted in ways contrary to the interests of the Church—as they frequently did—then the Pope, as head of the Church, could use a variety of means to keep them in line. As well as military force and punitive financial measures, the Pope had at his disposal the power of excommunication, which was widely used against unruly monarchs.
Lower down the social scale, millions of ordinary peasants worked on land owned by the Church. In addition, they were expected to pay tithes—a tenth of their income—to the Church. From the cradle to the grave, virtually every aspect of the life of the common people was in some way related to the Church. Births, marriages, deaths, religious feasts and festivals—all of the important stages of an average person's life in medieval Europe were shaped and controlled by the Church and its laws, doctrines, and customs.

The church was at the crux of people's lives in medieval Europe. People not only attended regular worship services at the church but also marked important events, such as baptisms, confirmations, weddings, and funerals, at the church. Most holidays were saints' days and were also religious in nature, and people's beliefs about life, death, sin, and the afterlife were largely determined by the church.
The church played a major role in the economy of medieval Europe; the church was a major landowner, and many peasants worked land that belonged to the church. In addition, people were required to pay one-tenth of their income, called a tithe, to the church, and many of these payments were made in animals or grain, which were stored in tithe barns owned by the church.
Cathedrals, constructed in cities, were the sites of the first universities, and monasteries (referred to as part of the "regular church," as opposed to the "secular church" where people worshipped) were the site of schools. Many great universities in Europe, including the Sorbonne in France, originally developed as schools associated with cathedrals. In addition, the church held political power, and technically, the Pope could even excommunicate kings and queens if they went against his dictates. Therefore, the church had a major political, social, and economic role in people's lives during medieval times.

What is the climax of "The Little Mermaid"?

The climax of "The Little Mermaid" occurs when she must choose between killing the prince to save her own life or sacrificing herself so he may live.
The climax of any story is the moment of greatest narrative tension. Usually, this involves the protagonist squaring off against the antagonist. This might be an individual that opposes their goals (usually called the villain) or an event they have to face. However, sometimes the antagonist is internal, something within the protagonist that they must overcome.
In "The Little Mermaid," the mermaid's antagonist turns out to be her own desire for the prince and an immortal soul. She wants this more than anything, to the point where she's willing to give up her voice, leave her family behind, and suffer great pain to achieve these goals. When the prince decides to marry another woman, these goals will be lost to her forever.
During the climax, the mermaid gets the chance to return to the ocean with her sisters on the condition that she stab the prince in the heart with an enchanted dagger. If she refuses, she will turn to sea foam and die without an immortal soul. The mermaid considers killing the prince, which creates suspense for the reader. However, her love for him overcomes her selfishness, and she chooses to die for him instead.
After that, the narrative tension winds down. The mermaid gets the chance to earn a soul with the help of the daughters of the air, which makes up the falling action. The resolution is that she gains a soul that will live on forever after.

In Hans Christian Andersen's "The Little Mermaid," the title character is motivated, out of love for the prince and out of a desire to attain an immortal soul (which mermaids do not possess), to make a deal with the sea witch to attain human legs so as to coexist with humans. As payment, the sea witch takes her tongue, removing her ability to speak or sing. Should the prince marry her, she would stand to receive an immortal soul, but should the prince marry someone else, then she would turn into sea foam.
Ultimately, in Andersen's tale, the mermaid's romantic hopes end in disappointment. While the prince has great affection for the mermaid, he has no desire to marry her, and by the end of the story, he is set to marry another. This brings about the climax of the tale, by which, after all her agony and torment, the mermaid finds herself face-to-face with her own mortality, aware that she will turn to sea foam with the coming morning.
It is in this context that the sisters return to her, having made their own deal with the sea witch, bartering their hair for a chance to save the mermaid's life. They present her with a knife, and tell her that if she were to drive the knife into the prince's heart, killing him, then she would return to her life as a mermaid. This is the dilemma that stands at the center of the story and serves as its key scene: she can kill the prince to save herself, or she can spare the prince, which means an immediate death with no hope of salvation. She tosses the knife away, surrendering to that fate.
The story ends on a hopeful note, however, as because of her suffering and sacrifice, she is transformed once again, not into a mermaid but into one of the "daughters of the air," who are given the chance to earn their souls through good deeds and service to the world.

The climax to The Little Mermaid (the movie) begins when Prince Eric and Ursula head out on the ship to get married, and Ariel decides to stop the wedding. In the scuffle that takes place, Ursula's spell over Ariel and Prince Eric is broken. He gets his mind back, and Ariel gets her voice back. They run toward each other and kiss. Unfortunately, the kiss comes a few seconds too late, and Ariel transforms back into a mermaid. Ursula then drags Ariel with her back into the ocean. Prince Eric heads out in a row boat to try and save her, and King Triton takes action as well. He overwrites Ariel's name on the contract and gives himself up in return. Ursula then becomes extremely huge and creates an enormous storm and whirlpool in the ocean as she taunts Ariel and just about anybody else who dares challenge her. Prince Eric then takes control of a ship that has a very pointy tip and steers it into Ursula's gut. This kills her and ends the storm. From this point forward, the story moves toward its resolution. Triton's power is restored to him, and he transforms Ariel into a human. She runs to Prince Eric, they get married, and they live happily ever after.

The Lottery (short story vs movie) In the 1996 film "The Lottery", what is the plot diagram (exposition, rising action, climax, falling action, resolution), types of characters (dynamic/static), setting (place/time), and conflict (main type? Internal or external?)?

One major difference that changes the story is that Shirley Jackson’s “The Lottery,” originally published in 1948 in The New Yorker, doesn’t focus on one main character. It’s an overview of the lottery from the perspective of a narrator. The film The Lottery focuses on a character who isn't only the sole protagonist but who also is an outsider in the town. Having an outsider experience the oddness of the town changes the tone of the story quite a bit when compared to a story where the lottery itself is normal and accepted by everyone in the narrative.
The exposition of a story is how background information is introduced into a story. It gives a reader information about the characters in the story and the location in which it takes place.
Most of the exposition in the short story centers around the idea of tradition. People gather in the field; they talk and joke while children play. They’re focused on returning to their days after the event. There’s a long portion focused on whether the box that holds the lottery papers should be remade or kept according to tradition, even though it’s old and broken-down.
The exposition in the movie is focused on Jason. He explains that he doesn’t remember his mother; he goes to visit his dying father and holds the bracelet of the mother he never knew, reflecting that she must have been small. In this way, the film shows how ignorant Jason is, both of his parents’ history and of New Hope itself. He doesn’t remember the town, her death, or where she’s buried. When his girlfriend leaves him, he’s free to leave and fulfill his father’s request to scatter his ashes on his mother’s grave.
The exposition in the film focuses more on the protagonist and less on the event itself. One reason for this is that New Hope is the initial mystery that drives the film, while the lottery itself is already known and accepted in the short story. The lottery is the central question in the story for the reader, while it’s both the answer to the initial mystery and the start of a new one in the film.
The rising action of a story is the series of events that happen to move the story along. It's what makes the story interesting and exciting; rising action captures the interest of the reader and keeps them moving through the story.
The rising action in Jackson’s short story is the drawing of initial lots in the lottery after stones are gathered and people are assembled. There’s discussion over who will draw for the absent people, and then the drawing begins. Jackson focuses on the subtle nerves of the viewers as the slips of paper are pulled and reviewed. The rising action comes to an end when the Hutchinson family gets the slip of paper with the black mark on it.
The rising action in the film focuses on the strange interactions Jason has with people in New Hope. He questions many things about the town, including the platform being built in the town square, the unwelcoming attitudes of every person in a position of authority, and the empty inn that the innkeepers claim is booked for the Fourth of July. At one point, the gas station attendant addresses Jason’s difficulty in burying his father in New Hope, saying, “They ain’t ever going to let any part of your father back in this town.” This is central to the mystery since people in town keep pretending—poorly—that they don’t know who Jason is or who his parents were.
Jason also suffers nightmares that flash back to his mother’s death in the town when he was a little boy. She was a past lottery loser who was stoned to death. His grandmother finds him at his mother’s grave and explains that someone switched his father’s ashes—and then points out that many people in New Hope have June 27th engraved as their death day on their tombstones. Jason realizes it’s due to the lottery. He’s then arrested and kept from leaving town.
Like the story, the film doesn’t come out and explain exactly what the lottery is. The viewer has to determine what’s happening the same way that the reader does in the story, based on context clues. The rising action is much more pronounced and drawn out over days in the film instead of taking place one summer morning. It also focuses on the mystery of the behavior of the residents of New Hope instead of only focusing on the lottery itself.
The rising action also contributes to the slow unveiling of the nature of the lottery to the reader, to Jason, and to the viewer. Once they’re aware of what the lottery is, the story builds to the climax, where the lottery takes place. In the case of the film, it also focuses on Jason’s arrest and awareness that he will have to be a part of the lottery. It continues to the initial drawing of lots, like the short story.
While the rising action of both stories ends in the same place —with the drawing of lots—the film has a much longer and more detailed plot. Because it focuses mainly on Jason and a few others in town, the viewer is more aware of the people in the movie than those in the story. They have personalities, connections, and backstories.
The climax of a story is the most dramatic point of the story. It’s when everything comes to the point the rising action was building to. It has the highest tension of the story.
In the short story, the climax of the story is when Tessie is selected from the Hutchinson family to be stoned to death. The children open their lots and see that they’re not chosen, and the father follows. Only the mother, Tessie, is left.
In the film, the climax begins when Jason is marched onto the stage to draw his ballot. He’s told to “draw his ballot” and then is marched off the stage while the mayor chooses his. The mayor reads the name of the last person to draw, and it’s Henry Watkins, the young gas station attendant. Once everyone has their ballots, they open them—and the innkeeper’s family is chosen. Felice and Maggie Dunbar walk onto the stage and choose the final ballots.
The difference between the climax of the short story and film is who is selected. It’s Tessie Hutchinson in the story and Maggie Dunbar in the film. They’re both mothers. However, Tessie is the one who complains that the drawing wasn’t fair in the story, while Maggie’s daughter, Felice, complains that it wasn’t fair in the film.
The falling action of a story is what happens after the climax. It’s the fallout from what happened during the climax and paves the way toward the resolution.
In the short story, the falling action shows Bill taking the paper from Tessie and proving to the crowd that she was selected. The assembled people then gather, take stones, and move to the place where they’ll stone Tessie to death.
In the film, the falling action shows the town picking up stones and preparing to stone Maggie. They then stone her to death. Afterwards, Maggie’s body is covered with a lace cloth, and Jason says, “God help you” to the people there before he turns to leave. He’s stopped by the men in the town, who chase him into the woods with guns.
Jason fights with the deputy and accidentally kills him. Then he escapes and tells people outside the town what he witnessed.
The falling action in the film extends beyond what happens in the story because there’s a different resolution. It includes the stoning of Maggie and Felice using a stone to hit her mother at the urging of the town preacher. It also covers Jason escaping from New Hope, a feature that wasn’t present in the story because there were no outside characters or dissenting people in the story.
The resolution of a story is the end of the story. It’s when the story is over and things are finished, when there’s a solution. Keep in mind that a resolution doesn’t have to be positive.
In the short story, the resolution is Tessie being stoned to death. The story ends with the words,

“It isn’t fair, it isn’t right,” Mrs. Hutchinson screamed, and then they were upon her.

There’s no turning back. Tessie is being killed, and no one is arguing against it.
In the film, the resolution is outside law enforcement not believing Jason. Felice is also unwilling to back his story and admit what happened. She lies and says her mother died of a stroke. Jason ends up imprisoned and unwilling to speak to a psychiatrist.
Characters can be either dynamic or static. To put it simply, dynamic characters change, while static characters stay the same.
In “The Lottery,” all the characters are dynamic. No one overtly questions the practice of the lottery. Even Tessie, who draws the final lot and is stoned to death, only questions the way the lottery is handled—not the practice itself. No one changes from beginning to end.
In the film, Jason changes during his experiences in New Hope. He’s still the same man at the end of the story, but he has a better idea of his past as well as his capabilities. When everyone else falls in line and kills Maggie, Jason opposes them and runs, escaping. He also stands up to the town, even though he isn’t believed. At the end, he also remembers throwing one of the rocks at his mother.
Felice Dunbar also changes—and then reverts—during the film. She begins as a member of the town dedicated to their traditions but later decides to leave with Jason and start a new life. When she’s stopped—and her mother is chosen for the lottery—she gives into pressure, stoning her mother and arguing for the cause of New Hope to Jason as she helps him escape at the end.
The setting of a story is the location or time in which it takes place.
In the short story, the entire narrative takes place in a small town with about 300 residents. Jackson never specifies the name of the town or what state it’s in. The entire story takes place in less than a couple of hours on June 27th.
In the movie, the primary action takes place in New Hope, Maine. Jason finds out where his mother is buried by looking at her death certificate in the doctor’s office of the hospital where his father died. Jason arrives in New Hope on June 24th, which is shown when the innkeeper reminds him he must be “out on the 26th,” which is two days after his arrival.
The conflict of a story is the struggle between two or more forces. It can take various forms. An internal struggle is one that takes place within a person. An external struggle takes place between a person and something outside themselves.
In the short story, the conflict is an external one. It’s man versus society. One person every year is killed because of a tradition that people barely remember the reason for. It’s this community tradition that leads to the death of Tessie Hutchinson.
In the movie, the conflict is the same. It’s man versus society. Jason literally fights with the authority figures—mayor, law enforcement, preacher—in New Hope to fulfill his father’s dying wish. He then opposes the tradition of the lottery, which is accepted by the community. Even Felice argues in favor of the tradition after her mother is killed.
Another major difference between the film and the story—one that affects all the other factors—is the tone of the story versus the tone of the film, especially at the beginning.
The story opens with a bright sunny day and people gathering. Children play. People chat. It’s a friendly crowd with no real gloom on the horizon.
The film opens with Jason, a tow truck driver, finding a dead man in the trunk of a car that wrecks into the one he’s towing. It continues and shows him in a hospital with flickering lights and a screaming man being guided through the halls. It’s dark and forbidding right from the start. Though New Hope looks lovely and sunny, it’s clear something dark lurks below the surface from the beginning, because the characters act strange and unwelcoming.
The differing tones make the two versions of the story very dissimilar. While the conclusion of Jackson’s story is shocking because of the light-hearted crowd and sunny day, the movie is more of a thriller throughout.
http://edtech2.boisestate.edu/weltys/502/conceptmap.html

How can I obtain a complete copy of all 635 issues of The Spectator?

The Spectator has actually made it extremely easy for you to find archived articles from older issues of the magazine. In fact, The Spectator has a digitized archive, fully available online, in which you can find articles from copies of the magazine published between 1828 and 2008, 180 years of magazines. This archive can be found here.
If you want to search by issue, rather than by topic, you can find the articles sorted by century and decade in the issue archive, which can be found here.
For issues of The Spectator from 2002 to the present day, you do not need to visit the digitized archive, which contains scanned copies of articles from physical magazines. Instead, you can simply visit the drop-down menu on the far right of the main magazine site or click here.
Eventually, you may find you hit a limit on the number of articles you are allowed to view, in which case you may need to subscribe using one of these plans.
It is not possible to acquire physical copies of every issue of the magazine ever printed, but the archiving that has been performed by the magazine is extremely extensive, and if there is an article you are looking for that has ever been published in The Spectator, it is possible to find it using the links above.

How does the author use setting to describe General Zaroff's "civilized world"? Support your answer with evidence from the selection.

When Sanger Rainsford first catches sight of General Zaroff's home, he sees "a lofty structure with pointed towers plunging upward into the gloom . . . a palatial chateau." This sounds like a very luxurious and civilized home on a remote island, a place for a wealthy individual who values privacy.
When he is shown to a bedroom, Rainsford sees "a huge, beam-ceilinged bedroom with a canopied bed big enough for six men." He is provided evening wear from "a London tailor who ordinarily cut and sewed for none below the rank of duke." 
The dining room where Zaroff entertains Rainsford for dinner is described as having a "medieval magnificence" with "oaken panels. . .[a] high ceiling. . . [and] vast refectory tables" befitting a wealthy, civilized individual who takes pride in providing an opulent setting for his guests.
The table's china, silver, crystal, and linen are the accouterments of a sophisticated host, and Rainsford enjoys a well-mixed cocktail, champagne, and filet mignon.  The quality of the home, its furnishings, and the hospitality Zaroff extends to Rainsford give the impression of a civilized world until Zaroff describes the barbaric hunt in which he expects Rainsford to participate as the quarry. 

What similarities are there between the Jungle Book and Gaiman's Graveyard Book?

The Graveyard Book, by Neil Gaiman, and The Jungle Book, by Rudyard Kipling, are quite similar in their themes and character choices. Though one takes place in a graveyard (presumably the very one in Sussex which inspired Gaiman) and the other in the jungles of South Asia. In fact, Gaiman deliberately mirrored the title and content of Kipling's work because it is a story he enjoyed and wanted to transform in his characteristic spooky style.
Both stories feature boys who are orphaned in early life but adopted into a surrogate family. For Mowgli, of The Jungle Book, his new family is more a pack of animals, including wolves, a bear, and a panther. For Bod, of The Graveyard Book, his surrogate family are the ghosts who dwell in the graveyard. In both stories, the boys are cared for and learn special skills from their new families. Though they do not live in human society, they learn to get on well enough. Both Bod and Mowgli do have some encounters with other humans and are apparently able to socialize in an appropriate way. 
The nature of the antagonist in both stories is very similar-- the fear that the one who orphaned the boys will return. Mowgli and his animal family are constantly evading the tiger Shere Khan, who is believed to have killed Mowgli's human family. For Bod, "the man Jack" has returned to hunt him down. In both, the protagonist overcomes their would-be killer. 
In the end, both Bod and Mowgli decide that they cannot live among their strange, surrogate families for ever. Bod's experiences at human school and brief friendships with other human children, as well as Mowgli's brief adoption into a human village, has shown them that there is more to life waiting for them. Even if it means giving up their supernatural or animal powers, both boys decide that their place is among other humans like them.

Calculus and Its Applications, Chapter 1, Review Exercises, Section Review Exercises, Problem 32

Below is the graph of the function $y = g(x)$. Determine the simplified difference quotient for
$f(x) = 2x^2 - 3$.



We have,
If $f(x) = 2x^2 - 3$, so

$
\begin{equation}
\begin{aligned}
f(x + h) &= 2(x + h)^2 -3 \\
\\
&= 2(x^2 + 2xh + h^2) - 3\\
\\
&= 2x^2 + 4xh + 2h^2 - 3
\end{aligned}
\end{equation}
$


Then,

$
\begin{equation}
\begin{aligned}
f(x + h) - f(x) &= 2x^2 + 4xh + 2h^2 - 3 - (2x^2 - 3) \\
\\
&= 2x^2 + 4xh + 2h^2 - 3 - 2x^2 + 3\\
\\
&= 4xh + 2h^2
\end{aligned}
\end{equation}
$


Thus,

$
\begin{equation}
\begin{aligned}
\frac{f(x + h) - f(x)}{h} &= \frac{4xh + 2h^2}{h}\\
\\
&= \frac{2h (2x + h)}{h}\\
\\
&= 2(2x + h)
\end{aligned}
\end{equation}
$

What river forms the border between the United States and Mexico?

The Rio Grande- Spanish for "big river-" has its source in the mountains of Colorado, runs through New Mexico, Texas, and the country of Mexico, and empties into the Gulf of Mexico. Along the way, this river marks part of the border between the United States and Mexico.
In the past, Mexico territory included much of what is today the southwest United States. For much of history, the Rio Grande did not represent a national border, rather a geographic border between the northerly and central parts of Mexico. In 1848, the United States acquired much of the American Southwest through the Treat of Guadelupe, which meant reorganizing national borders. The Rio Grande was a natural choice for demarcating the border because of its geographic significance.
https://www.britannica.com/place/Southwest-region

https://www.nps.gov/rigr/index.htm

College Algebra, Chapter 1, 1.1, Section 1.1, Problem 32

The equation $\displaystyle \frac{1}{t-1} + \frac{t}{3t- 2} = \frac{1}{2} $ is either linear or equivalent to a linear equation. Solve the equation

$
\begin{equation}
\begin{aligned}
\frac{1}{t-1} + \frac{t}{3t-2} &= \frac{1}{2} && \text{Get the LCD of the left side}\\
\\
\frac{3t-2+t(t-1)}{(t-1)(3t-2)} &= \frac{1}{2} && \text{Simplify}\\
\\
\frac{3t-2+t^2-t}{(t-1)(3t-2)} &= \frac{1}{2} && \text{Combine like terms}\\
\\
\frac{t^2 + 2t - 2}{(t-1)(3t-2)} &= \frac{1}{2} && \text{Factor the numerator}\\
\\
\frac{\cancel{(t-1)}(t+2)}{\cancel{(t-1)}(3t-2)} &= \frac{1}{2} && \text{Cancel out like terms}\\
\\
\frac{t+2}{3t-2} &= \frac{1}{2} && \text{Multiply both sides by } 2(3t-2)\\
\\
2 (\cancel{3t-2}) & \left[ \frac{t+2}{\cancel{3t-2}} = \frac{1}{\cancel{2}} \right] \cancel{2} (3t - 2) && \text{Simplify}\\
\\
2(t+2) &= 3t -2 && \text{Apply Distributive property}\\
\\
2t +4 &= 3t - 2&& \text{Combine like terms}\\
\\
2t - 3t &= -4 -2 && \text{Simplify}\\
\\
-t &= -6 && \text{Multiply both sides by -1}\\
\\
-1 & [ -t = -6 ] -1 && \text{Simplify}\\
\\
t &= 6
\end{aligned}
\end{equation}
$

In The Big Short, how did the real estate industry, banks, and investment bankers break every ethical rule, including an obligation to have personal integrity, be honest, and take responsibility for their actions? What moral philosophy did the bankers use to justify their actions and how did it lead them to behave as they did? What are two moral philosophies that would have led to a more ethical result?

In the movie, the banks and investment bankers basically collude to enrich themselves at the expense of investors.
The main culprit in this fiasco is one Michael Burry, a hedge-fund manager (played by Christian Bale). It is the year 2005, and Michael realizes that the housing market is sitting on a bubble which will eventually burst. Rather than warn the public, Michael decides to cash in on the crash when it happens. Through his research, he realizes the housing market has been supported by a glut of high-risk subprime loans. Subprime loans are typically made to investors with less-than-stellar credit, and the interest rates are usually (and sometimes substantially) higher than prime rates. These loans allow individuals with poor credit to buy houses or infuse some much-needed cash into their businesses.
These loans are extremely risky, though. When borrowers make mortgage payments on time, the loans can be extremely profitable bond assets. Because of the nature of the loan, defaults can pose an immediate threat to any investor's financial viability. Noting this, Michael decides to create what is called a default-swap market in which he can leverage his prediction of the bonds failing into a profitable enterprise. A default-swap market involves a transfer of credit risk between two parties.
The buyer is protected in case of a default or credit downgrade; he pays the seller (who assumes the credit risk) an insurance premium for this protection. For his part, the seller only needs to pay up if a definitive, negative credit event occurs. Read more about credit default swap markets here. Michael establishes a default-swap market where he bets on the probability that subprime mortgage-backed securities will fail. He is joined by Mark Baum (played by Steve Carrell) in his project.
When the housing bubble does eventually burst, Michael makes over $2.5 billion. The bursting of the housing bubble refers to a financial fallout when large numbers of individuals default on their subprime mortgages.
In the meantime, the banks and bankers Michael colludes with are guilty of ethical violations as well. They work stealthily with credit rating companies to maintain their AAA ratings until they can sell off losing positions. Michael pays the banks substantial insurance premiums in the credit-swap market, and he uses his investors' money to do this. When his investors complain and try to withdraw their money, Michael places a freeze on withdrawals. Despite this, Michael is able to profit immeasurably when the housing bubble bursts, and he manages to earn more than 500% profit for those investors who remain loyal to him throughout the financial fiasco.
On the other hand, those investors who had no inkling of the dangers of (subprime) mortgage-backed securities reaped excessive losses when the housing market destabilized. Many lost their homes and 401(K) investments. Because banks colluded with ratings companies to protect their AAA ratings on subprime loans, many investors were unaware of the risks they incurred in owning subprime-backed investments.
The moral philosophy the bankers used to justify their actions would likely be individual or moral relativism. That's the belief that all viewpoints are equally acceptable. So, an individual who is a relativist sets his own values (whatever they may be) and lives by them. In Michael Burry's case, his main aim is to make money. Although he comes to regret his actions, his initial rationalization is that wealth is a worthy goal. He profits handsomely from the financial crisis, as do his investors (he thinks this is a good thing), but he comes to realize that his willful participation in fraud has ruined many lives.
The banks and bankers who work for them justify their actions in the same way. They sell the subprime loans on the secondary market to unsuspecting investors and transfer the risks of these loans to investors. The banks rationalize that the subprime loans they originally provided helped many low-income buyers purchase their own homes.
In my opinion, two moral philosophies which would have produced more ethical results would be deontology and consequentialist utilitarianism. Deontology rests on every individual's obligation or duty to the society he/ she lives in; this moral philosophy focuses on the rightness or wrongness of one's actions. On the other hand, consequentialism pertains to the consequences of one's actions. Utilitarians believes that the most moral actions rest in bringing the greatest good to the greatest number of people.
For more, please read Deontological ethics (which also discusses deontology's foil: consequentialism).
https://www.investopedia.com/articles/investing/020115/big-short-explained.asp

https://www.philosophybasics.com/branch_deontology.html

https://www.thetruthaboutmortgage.com/what-caused-the-mortgage-crisis/

y = 9 - |x| , y=0 Find b such that the line y = b divides the region bounded by the graphs of the equations into two regions of equal area.

Given ,
y = 9-|x| , y = 0
first let us find the total area of the bounded by the curves.
so we shall proceed as follows
as given ,
y = 9-|x| , y = 0
=> 9-|x|=0
=> |x| -9 =0
=> |x|=9
so x=+-9
 
the the area of the region is = int _-9 ^9 (9-|x| -0) dx
=>int _-9 ^0 (9+x -0) dx+int _0 ^9 (9-x -0) dx
=>[9x+x^2 /2]_-9 ^0 + [9x-x^2/2]_0 ^9
=>[0]-[-81+81/2] +[81-81/2]-[0]
=>81/2 +81/2 =81
So now we have  to find the horizonal line that splits the region into two regions with area 81/2
as when the line y=b intersects the curve y=9-|x| then the area bounded is 81,so
let us solve this as follows
first we shall find the intersecting points
as ,
9-|x|=b
|x|= 9-b
x=+-(9-b)
so the area bound by these curves y=b and y=9-|x| is as follows
A= int _-(9-b) ^(9-b) (9-|x|-b)dx = 81/2
=>int _-(9-b) ^0 (9+x-b)dx +int _0 ^(9-b) (9-x-b)dx =81/2
=>[9x+x^2/2-bx]_-(9-b) ^0 +[9x-x^2/2-bx]_0 ^(9-b) = 81/2
=>[0]-[9(-(9-b))+(-(9-b))^2 /2-b(-(9-b))]+
[9((9-b))-((9-b))^2/2-b((9-b))]-[0]=81/2
=> [9((9-b))-((9-b))^2/2-b((9-b))]
-[9(-(9-b))+(-(9-b))^2/2 -b(-(9-b))]=81/2
let t= 9-b
so
=> [9(t)-(t)^2/2 -b(t)] -[9(-t)+(-t)^2/2 -b(-t)]=81/2
=>[9t-t^2/2 -bt]+[9t-t^2/2 -bt]=81/2
=>18t-t^2-2bt =81/2
but we know half the Area of the region between y=9-|x|,y=0 curves =81/2
so now ,
18t-t^2-2bt =81/2
18t-2bt-t^2 = 81/2
=>t(18-2b)-t^2=81/2
=> t^2=t(18-2b)-81/2
=>t^2 -t(18-2b)+81/2=0
this is like  quadratic equation
ax^2+bx+c=0
so t = (-b+-sqrt(b^2-4ac))/2a
  =(18-2b+-sqrt((-(18-2b))^2-4*(81/2)))/2
but
t=9-b
so,
9-b=(18-2b+-sqrt((-(18-2b))^2-4*(81/2)))/2
=> 18-2b=(18-2b+-sqrt((-(18-2b))^2-4*(81/2)))
=>+-sqrt((-(18-2b))^2-4*(81/2))=0
=>sqrt((-(18-2b))^2-4*(81/2))=0
=>(-(18-2b))^2-4*(81/2)=0
 
=>(-(18-2b))^2=4*(81/2)
=>(-(18-2b))^2=2*(81)
=>(-(18-2b))= +- sqrt(2) *9
=> -18+2b=+-9sqrt(2)
=>2b=+-9sqrt(2)+18
=>b=(18+-9sqrt(2))/2
so b= (18+-9sqrt(2))/2

College Algebra, Chapter 5, 5.3, Section 5.3, Problem 14

Evaluate the expression $\displaystyle \log_3 100 - \log_3 18 - \log_3 50$


$
\begin{equation}
\begin{aligned}

\log_3 100 - \log_3 18 - \log_3 50 =& \log_3 100 - (\log_3 18 + \log_3 50)
&&
\\
\\
\log_3 100 - \log_3 18 - \log_3 50 =& \log_3 100 - \log_3 (18 \cdot 50)
&& \text{Law of Logarithms } \log_a (AB) = \log_a A + \log_a B
\\
\\
\log_3 100 - \log_3 18 - \log_3 50 =& \log_3 \left( \frac{100}{900} \right)
&& \text{Law of Logarithms } \log_a \left( \frac{A}{B} \right) = \log_a A - \log_a B
\\
\\
\log_3 100 - \log_3 18 - \log_3 50 =& \log_3 \left( \frac{1}{9} \right)
&& \text{Simplify}
\\
\\
\log_3 100 - \log_3 18 - \log_3 50 =& -2
&& \text{Because } 3^{-2} = \frac{1}{9}

\end{aligned}
\end{equation}
$

Why is Shylock is said to be devil?

In Shakespeare's play The Merchant of Venice, Shylock is the Jewish antagonist, who is portrayed as a greedy, malevolent moneylender. The play is set in sixteenth-century Venice, which was a period when the majority Christian population discriminated against Jewish citizens because they did not believe that Jesus Christ was the Messiah. The Christian characters in the play view Shylock with contempt and despise him for his moneylending practices. They view Shylock as a greedy usurer who unjustly charges citizens interest for borrowing his money. Antonio refers to Shylock as the devil in act 1, scene 3 by telling his friend,

Mark you this, Bassanio, The devil can cite Scripture for his purpose. An evil soul producing holy witness Is like a villain with a smiling cheek, A goodly apple rotten at the heart (Shakespeare, 1.3.95-99).

Antonio's prejudice against Jewish citizens and his contempt for Shylock's taboo lending practices are the reason he refers to Shylock as the devil. Antonio believes that, similar to the devil, Shylock is a crafty, shrewd person who cannot be trusted. The fact that Shylock does not acknowledge that Jesus is the Messiah is an additional reason Antonio compares him to the devil. Despite Antonio's views and Shylock's nefarious attitude, the audience sympathizes with Shylock to a degree because he is a victim of prejudice.

From the articles I-XXVII of the US Constitution, what are 5 examples of violations of popular sovereignty, political equality, political liberty, justice and/or democracy?

There are only seven articles in the United States Constitution. There are twenty-seven amendments to the Constitution. There are several ways in which the United States Constitution violates popular sovereignty, political equality, political liberty, justice, and democracy.
One example of how the United States Constitution violates popular sovereignty is the process of how we elect our President. The Electoral College actually chooses our President. There have been a few instances where a candidate won the popular vote but lost the vote in the Electoral College. This happened in the presidential election of 2016.
An example of how political equality is violated can be seen with the United States Senate. Each state, regardless of its population, has two senators. As a result, senators from states with large populations represent more people than senators from states with smaller populations.
Several examples of the violation of democracy and political liberty are that there are limits on who can run for the Congress and for the presidency. A person must be at 25 years old to run for the House of Representatives. To run for the United States Senate, a person must be at least 30 years. To run for the presidency, a person must be at least 35 years old.
Our Supreme Court justices are appointed and confirmed by the Senate. This violates the idea of popular sovereignty and may violate the concept of justice. When the Senate refused to vote on the appointment of Supreme Court nominee Merrick Garland because he was appointed in the last year of President Obama’s term, many people felt this was a violation of justice.
All of these points are examples of violations of popular sovereignty, political equality, political liberty, justice, and democracy.
http://constitutionus.com/

First of all, please note that there are not 27 articles to the Constitution of the United States.  Instead, there are only seven articles.  In addition, there are 27 amendments that have been ratified since the Constitution was created.  It is not clear whether you mean that we should find violations within the Constitution proper or whether you are including all the amendments.  Here are some violations:
Article I, Section 2 says that people cannot be elected to the House of Representatives if they are not at least 25 years old.  This violates popular sovereignty because it does not allow people to vote for whomever they want.  It also violates political liberty because it discriminates against people under 25 years of age.
Article I, Section 3, gives two senators to each state.  This violates political equality.  It means (today) that all the 38 million people in California are only represented by two senators, just the same as the 580,000 people in Wyoming.  This gives each person in Wyoming much more say over the Senate than each person in California.
This same article says a person cannot be a senator unless they are at least 30 years old.  This violates the same things that I mentioned in the first bulleted point.
Article I, Section 9 lists all sorts of things that the Congress cannot do.  This violates popular sovereignty.  The government should be able to do whatever the people want.  If the people want the government to make an ex post facto law, the idea of popular sovereignty says they should get their way.  Every amendment to the Constitution that says “Congress shall make no law…” does this as well.
Article II, Section 1 creates the Electoral College.  This violates popular sovereignty because it does not allow the people to elect the president directly.
All of these are, arguably, violations of aspects of democracy.
https://www.archives.gov/founding-docs

What would be the specific purpose, goals, and objectives of a manager-led team in a human services agency that provides support and services for individuals with intellectual disabilities?

The purpose in a human services agency dedicated to serving individuals with intellectual disabilities is to provide "prevention, treatment employment and support" (e.g., emergency intervention, referral services) in collaboration with other community institutions (e.g., schools, hospitals) as needed by community members (Hanover Community Services). Relevant goals are to connect each individual with the services that are needed in a supportive, timely and appropriate manner. Relevant objectives, which meet the broader service board vision, are to work collaboratively in the community and through partnership with individuals to deliver the help needed through a process that is welcoming, friendly and accessible (Hanover).Intellectual disabilities are defined as disabilities characterized by "significant limitations in both intellectual functioning and in adaptive behavior" (AAIDD). The concept of intellectual functioning comprises functions such as problem solving, cognitive competence, reasoning and learning. The concept of adaptive behavior comprises everyday conceptual skills (e.g., money skills, and number skills), social skills (e.g., rule following, personal interactions), and practical skills (e.g., travel, grooming, safety) (AAIDD). The purpose, goals and objectives applicable to a general human services board, which provides services and support for a broader range of needs (e.g., developmentally delayed infants, drug and substance abuse), are relevant to a community services board that provides support and services for individuals with intellectual disabilities but with defined purpose, goals and objectives focused on and adjusted for the segment of the community population with intellectual disability. A manager-led team would operate under the same broad objectives that govern the entire board and under the same community-directed purpose, which is to provide prevention, intervention, referral and support. The manager-led team goals would detail specifics relevant to daily operation of the human services center, such as intake, emergency services and referral services. Team members, with special knowledge of differing aspects, would bring knowledge and experience to the team and attain specific steps, milestones and goals defined by the manager and fine-tuned through input of the other team members. Some team goals, among others, would be to provide services and support for independent living skills (e.g., travel, money, grooming), learning skills (e.g., literacy, education) and social skills (e.g., friendships, rule following).
American Association of Intellectual and Development Disabilities (AAIDD).
General Human Services Community Services Boards, Fairfax, VA; Hanover, VA.
National Organization for Human Services (NOHS)
"Developing and Sustaining High-Performance Work Teams," Society for Human Resource Management (SHRM)
https://www.aaidd.org/intellectual-disability/definition

https://www.nationalhumanservices.org/what-is-human-services

College Algebra, Chapter 4, Chapter Review, Section Review, Problem 20

Graph the polynomial $P(x) = x^5 + x^4 - 7x^3 - x^2 + 6x + 3$ by using a graphing device. Find the $x$ and $y$ intercepts and the coordinates of all local extrema. Describe the end behavior of the polynomial.







Based from the graph, the $x$ intercepts can be approximated as $-3.05, 1.35$ and $1.80$. On the other hand, the value of the $y$ intercept is $3$. Also, the coordinates of the local maxima are $(-2.45, 33)$ and $(0.5, 5)$. While the coordinates of the local minima are $(-0.60, 0.80)$ and $(1.60, -1.75)$. More over, the function has an end behavior of $y \to \infty$ as $x \to \infty$ and $y \to - \infty$ as $x \to - \infty$.

How/in what ways does Polonius represent a snake?

Hamlet describes the word as

[...] an unweeded gardenThat grows to seed. Things rank and gross in naturePossess it merely. (1.2.135-137)

Such a description might make us think of the Garden of Eden—certainly religious references abound in the play— specifically Paradise after the fall of Adam and Eve through the machinations of the Devil who tempts Eve while in the form of a snake. In the play, Polonius's involvement in the relationship between Hamlet and Ophelia destroys it too; Polonius tells Ophelia that she must break off her relationship with Hamlet because Hamlet feels only lust for her and could not marry her even if he wanted to. It turns out that this is not true (Gertrude later expresses her desire that Ophelia would have been in daughter-in-law)—just as what the snake tells Eve is not true—and it initiates a sequence of events that leads to Ophelia's destruction as well as Hamlet's. It seems especially fitting that Ophelia passes out flowers just before the dies and then dies while she is hanging flower garlands. Her Eden was destroyed by Polonius's involvement.

Snakes are cold-blooded creatures that tend to hide away to regulate their temperature. They are traditionally considered devious because they sneak up on prey and strike, often poisoning the victim before it knows what is happening.
Polonius can likewise be seen as a snake because he is a cold-blooded courtier who will do whatever it takes to advance his career. He is devious when he sends his servant Reynaldo to spy on Laertes in France. Polonius also spies on Hamlet. The first time, he does so with Claudius to try to determine if Hamlet's strange behavior is due to his being in love with Ophelia. The second time he spies on Hamlet, Hamlet mistakes him for Claudius and kills Polonius.
As far as Hamlet is concerned, Polonius is not a trustworthy figure because he is a sycophant, a devious person who will lie and flatter to get ahead.

At the end, what is Phillip studying?

I think that this question is asking about events at the very end of the novel. In my text, this information is found on the last page. The final chapter of the book moves quickly. When the chapter starts, Phillip is still stranded on the island. He is rescued by a naval destroyer that just happens to put crew ashore on the small cay. Phillip is rushed to a hospital in Panama, his mom and dad arrive, he is moved to a hospital in New York for a series of eye surgeries, his sight is restored, and he and his family return to Curacao. The war ends, and Phillip's family moves again. It's not until after all of that happens that Phillip tells his readers that he has "spent many hours" looking at and studying charts of the Caribbean. We are told that he has found many islands in the area, and Phillip has even found the Devil's mouth. Presumably, Phillip is looking for the small cay that he and Timothy survived on for all of those months. Phillip's goal is to go back to the island and visit Timothy's grave.

Someday, I'll charter a schooner out of Panama and explore the Devil's Mouth. I hope to find the lonely little island where Timothy is buried.
Maybe I won't know it by sight, but when I go ashore and close my eyes, I'll know this was our own cay. I'll walk along east beach and out to the reef. I'll go up the hill to the row of palm trees and stand by his grave.
I'll say, "Dis b'dat outrageous cay, eh, Timothy?"

Why is evolution a hard topic to cover?

Evolution is a difficult concept to cover because it is contrary to popular religious teachings.
Evolution itself is a rather simple thing to teach. All living things have a common ancestor. Adaptation occurs over time as natural pressures make certain genes advantageous; this is natural selection. Speciation is when a line from one species has adapted to the point of being different from its parent species. Teaching evolution itself, even in depth, can be done very efficiently.
People might resist evolution because they believe a real divine power makes more sense. For example, in the American South, many fundamental Christians believe in Genesis theory, where God created the world over seven days, the Earth is only 6000 years old, and God once sent a massive flood to destroy the world. These Christians will lobby their state and city governments to ensure that what they believe is taught instead of or alongside what they think is a lie. Because they have lobbying power in these places, these individuals can be very successful.
Most schools are nervous about teaching evolution, as it can be a touchy subject. This means that they will either simply not cover it or present a religious view on the subject at the same time, implying both are credible theories.

College Algebra, Chapter 1, 1.2, Section 1.2, Problem 18

Express the value (in cents) of the change in a purse that contains twice as many nickels as pennies, four more dimes than nickels, and as many quarters as dimes and nickels combined. Suppose that $p$ = number of pennies.

Let $v$ be the value in cents of the change, so if we translate each statement in to algebra, we have

$
\begin{array}{|c|c|}
\hline\\
\text{In words} & \text{In Algebra} \\
\hline\\
\text{twice as many nickels as pennies} & n = 2p \\
\hline\\
\text{four more dimes them nickels} & d = 4 + n \\
\hline\\
\text{as many quarters as dimes and nickels combined} & q = d + n\\
\hline
\end{array}
$

Thus,


$
\begin{equation}
\begin{aligned}

v =& n + d + q
&&
\\
\\
v =& 2p + 4 + n + d + n
&& \text{Combine like terms}
\\
\\
v =& 2p + 2n + d + 4
&& \text{Make $n$ and $d$ in terms of $p$}
\\
\\
v =& 2p + 2(2p) + 4 + n + 4
&& \text{Simplify}
\\
\\
v =& 2p + 4p + n + 8
&& \text{Make $n$ in terms of $p$}
\\
\\
v =& 2p + 4p + (2p) + 8
&& \text{Combine like terms}
\\
\\
v =& 8p + 8
&&

\end{aligned}
\end{equation}
$

h(x)=(5x+3)/(-x+16) Graph the function. State the domain and range.

To be able to graph the rational function y =(5x+3)/(-x+16) , we solve for possible asymptotes.
Vertical asymptote exists at x=a that will satisfy D(x)=0 on a rational function f(x)= (N(x))/(D(x)) . To solve for the vertical asymptote, we equate the expression at denominator side to 0 and solve for x .
In y =(5x+3)/(-x+16) , the D(x) =-x+16 .
Then, D(x) =0  will be:
-x+16=0
x=16
The vertical asymptote exists at x=16 .
To determine the horizontal asymptote for a given function: f(x) = (ax^n+...)/(bx^m+...) , we follow the conditions:
when n lt m    horizontal asymptote: y=0
        n=m    horizontal asymptote:  y =a/b
        ngtm      horizontal asymptote: NONE
In y =(5x+3)/(-x+16) , the leading terms are ax^n=5x or 5x^1 and bx^m=-x or -1x^1 . The values n =1 and m=1 satisfy the condition: n=m. Then, horizontal asymptote  exists at y=5/(-1)  or y =-5 .
To solve for possible y-intercept, we plug-in x=0 and solve for y .
y =(5*0+3)/(-0+16)
y =(0+ 3)/(0+16)
y = 3/16 or 0.188  (approximated value)
Then,  y-intercept is located at a point (0, 0.188) .
To solve for possible x-intercept, we plug-in y=0 and solve for x .
0 =(5x+3)/(-x+16)
0*(-x+16) =(5x+3)/(-x+16)*(-x+16)
0 =5x+3
-3=5x
x=(-3)/5= -0.6
Then, x-intercept is located at a point (-0.6,0) .
Solve for additional points as needed to sketch the graph.
When x=11 , the y = (5*11+3)/(-11+16)=58/5=11.6 . point: (11,11.6)
When x=20 , the y =(5*20+3)/(-20+16)=103/(-4)=-25.75 . point: (20,-25.75)
When x=30 , the y =(5*30+3)/(-30+16) =153/(-14)~~-11 . point: (30,-11)
When x=-26, the y =(5(-26)+3)/(-(-26)+16) =-127/42~~-3.024. point:(-26,-3.024)
 
As shown on the graph attached below, the domain: (-oo, 16)uu(16,oo)
and range: (-oo,-5)uu(-5,oo).
The domain of the function is based on the possible values of x. The x=16 excluded due to the vertical asymptote.
The range of the function is based on the possible values of y. The y=-5 is excluded due to the horizontal asymptote. 

In Blade Runner, how does Deckard show pessimism?

The lack of hope in the world and his place in it represents Deckard's pessimism in Blade Runner.
Deckard's lack of optimism is seen in his life and the world around him. His pessimism is evident his job:  "They don't advertise for killers in the newspaper. That was my profession. Ex-cop. Ex-blade runner. Ex-killer." Deckard does not use any rationalization to justify what he does. He understands his function in the world is one of negation: "The report read 'Routine retirement of a replicant.'  That didn't make me feel any better about shooting a woman in the back."  
Deckard's negative tone is a result of the world in which he lives.   It is a setting where human emotions can be simulated emotionally cushioned" and simulated, corporations can do whatever they wish without any form of governmental limitation, and the police have the authority to kill anyone deemed a replicant. The film's cinematography enhances this through its use of dark and shadows, conveying something sinister and unsettling about the world of the future.
Deckard is unable to convey restoration and hope because the world in which he lives lacks these elements.  He cannot be a force of redemption in changing the world for the better.  Rather, he can only escape it.  Deckard's pessimism is rooted in a world that lacks hope. 

An AC current is driven around a loop of wire. Suppose the amplitude and frequency of the current are both doubled. By what factor does the power radiated by the antenna increase?

This is a magnetic dipole. A magnetic dipole in a vacuum radiates an average power by the following relation.
ltPgt =(mu_0 m_0^2 omega^4)/(12 pi c^3)
mu_0 is the magnetic permeability of a vacuum, m_0 is the average magnetic dipole moment, omega is the angular frequency, and c is the speed of light.
First we know that m_0=Ia , where I is the current and a is the area of the loop. We want to know (< P_f >) / (< P_i >) .
()/()=(mu_0 I_f^2 a^2 omega_f^4)/(12 pi c^3)*(12 pi c^3)/(mu_0 I_i^2 a^2 omega_i^4)=(I_f omega_f^4)/(I_i omega_i^4)
Plug in the changes between the final and initial configurations.
()/()=(I_f^2 omega_f^4)/(I_i^2 omega_i^4)=((2I_i)^2 (2omega_i)^4)/(I_i^2 omega_i^4)=2^6
The antenna radiates 2^6 times more power than initially.

how were jews treated when they were lined up outside

The first time the Jews are given the directive to file into lines outside takes place in chapter 1 when the Hungarian police prepare the Jewish citizens of Sighet for transports to Buna. Elie recalls waking up and hearing the Hungarian police yelling at his neighbors to evacuate their homes immediately. Once the Jewish citizens are standing outside, the Hungarian police use their rifle butts and clubs indiscriminately to strike anyone in sight. One by one each house is emptied, and the Jewish citizens stand with their luggage in the street. Elie also recalls the oppressive heat that day and remembers children crying for water. Fortunately, some of the policemen secretly filled jugs of water to give to the Jewish prisoners standing in the street. Later, Elie watches as his Jewish neighbors slowly walk in a procession towards the gate of the ghetto, which reminds him of the Babylonian captivity. Elie also says,

"They [Jews citizens of Sighet] passed me by, like beaten dogs, with never a glance in my direction" (Wiesel, 42).

The next day, Elie and his family are forced to stand outside and form a line. They are also subjected to the intense yelling and constant demands from the aggressive policemen, who force them to walk faster while simultaneously threatening them. Overall, the Jewish citizens are treated terribly and subjected to violence, intimidation, and exhaustion while they line up outside of the ghettos in chapter 1.

I think you're referring to the evacuation of the Buna concentration camp, in which Elie, his father, and many more Jewish prisoners were forced to run through snow to Gleiwitz, which was about 13 miles away. The weather conditions were harsh, the physical state of the Jewish prisoners was poor due to malnourishment and constant grueling work, and the prisoners did not have proper clothing or shoes to traipse through winter weather, so we can safely say that the Jews were treated terribly in this instance, just as they are throughout the book. Many people died on this two-night death march, and upon arriving in Gliewitz, they were subjected to stifling, cramped quarters in which many were crushed to death, as well as a period of three days without food or water. Freezing temperatures, starvation, beatings, shootings, and a cruelly quick pace are just a few of the inhumane conditions that plagued this particular group of prisoners.

What are the literary devices in "An Unstamped Letter in Our Rural Letter Box" by Robert Frost?

Another lovely simile is created when the speaker says,

There I elected to demurBeneath a low-slung juniperThat like a blanket on my chinKept some dew out and some heat in,Yet left me freely face to faceAll night with universal space.

In the simile, the speaker compares the low-slung juniper, under which he decides to sleep, to a blanket that not only helps keep him warm, but also keeps some of the night's dew off of him. Further, in the passage above, there is also an example of personification. When the speaker says that he is left free to be face to face with universal space, he gives space the human quality of having a face. The speaker also personifies his memories when he describes them:

Inside the brainTwo memories that long had lainNow quivered toward each other, lipped Together, and together slipped.

The speaker seems to give these memories the physical ability to lie down, as a person might, the ability to quiver while moving toward one another, and the ability to kiss as they lipped together. Obviously, memories are not tangible objects that can move and shake and kiss, but they sound like two lovers here.
The speaker also employs irony by suggesting that although he is a "tramp," he has experienced many advantages that his "involuntary host" may not have. For one, "sleeping out" has given this homeless speaker the opportunity to witness the spectacular beauties of nature, like the "coalesc[ing]" of two stars in the middle of the night. We would not expect a homeless person to count himself as lucky as, or even luckier than, a person with a nice warm bed in a cozy house, but he does.

The most notable literary devices in Robert Frost’s "An Unstamped Letter in Our Rural Letter Box" are rhyming couplets, similes, and diction.
Frost uses rhyming couplets (two lines of roughly the same length that end in a rhyme) throughout most of the poem.
Frost changes his rhyme scheme for lines 43-47:

43 You have had your advantages.
44 Things must have happened to you, yes,
45 And have occurred to you no doubt,
46 If not indeed from sleeping out,
47 Then from the work you went about

He ends lines 43 and 44 with "advantages" and "yes." This could be considered an imperfect rhyme (words that have a similar sound but not identical sounds). Frost further disrupts his previous pattern of couplets with lines 45, 46 and 47. Instead of a couplet, Frost has three consecutive lines that end in a rhyme.
In lines 7 and 8, Frost uses a simile: "There, pointed like the pip of spades, / The young spruce made a suite of glades." He compares the "young spruce" to "spades."
In line 10, Frost again uses simile: "The place was like a city park." He compares this section of woods to a "city park."
Lastly, Frost’s language choice is highlighted in line 50 when he uses the Latin legal term "forma pauperis."

Why does the girl say, ”we are seven”?

In this poem by William Wordsworth, the speaker meets "a little cottage Girl" and strikes up a conversation with her. He asks her the simple question one might routinely ask a child, "Sisters and brothers, little Maid, how many may you be?" The girl tells him "Seven are we," but goes on to say that two live in Conway, a seaport village in North Wales, and two "are gone to sea," presumably serving in the British Navy. She then easily drops the fact that two of her siblings are buried in the church-yard near her home. The speaker quickly does the math and realizes that the child has four siblings still living, which makes the answer to his question five, not seven.
He presses for an explanation. She then describes how she incorporates the dead siblings into her daily activities. Since their graves are directly outside the back door of her cottage, she often brings her sewing tasks to their gravesides and sits there singing to them as she sews. Additionally, she often brings her supper outside to eat beside their graves. The speaker tries to get the child to recalculate her original answer, reminding her that two of her siblings are in heaven. The final stanza states that "the little Maid would have her will, and said, 'Nay, we are seven!'" Clearly, she still numbers her dead siblings among her family members, and considering how frequently she includes them in her daily life, it makes sense. To think of them that way is "her will." She wants to keep them in her heart, and she deliberately does, so her arithmetic is accurate.

How is "Upon my head they placed a fruitless crown" portrayed through the character of Macbeth?

When Macbeth murders Duncan, he can no longer go back to the point when his conscience was more or less clear. He has stepped into the realm of darkness, where he is tortured by his thoughts of insecurity and doubt. The witches' prophecy becomes engraved in his mind, and he cannot help but remember the witches said Banquo's sons would inherit the throne one day. This news greatly perturbs him:

They hail'd him father to a line of kings:Upon my head they placed a fruitless crown,And put a barren sceptre in my gripe,Thence to be wrench'd with an unlineal hand,No son of mine succeeding. 

Although Macbeth gains power when he takes the throne, in a way, he loses more. He loses his peace, compassion, and all sense of right and wrong. He becomes tormented by his insecurities and his belief that others will attempt to dethrone him. 
Macbeth takes the witches' prophecy too seriously and decides to kill Banquo and his son. This will lead to many more misdeeds on Macbeth's part because he has forever lost his common sense. He wants to get rid of anyone who could potentially harm him in any way. This will lead to his imminent downfall.

Single Variable Calculus, Chapter 3, 3.4, Section 3.4, Problem 49

Differentiate each Trigonometric Identity to obtain new identity.
$\displaystyle \text{(a) }\tan x = \frac{\sin x}{\cos x} \qquad \text{(b) } \sec x = \frac{1}{\cos x} \qquad \text{(c) } \sin x + \cos x = \frac{1+ \cot x}{\csc x} $

$
\begin{equation}
\begin{aligned}
\text{a.) } \tan x &= \frac{\sin x}{\cos x}\\
\\
\frac{d}{dx}(\tan x) &= \frac{\cos x \frac{d}{dx} \sin x - \sin x \frac{d}{dx} \cos x}{(\cos x)^2} && \text{Applying quotient rule}\\
\\
\sec ^2 x &= \frac{\cos x(\cos x) - \sin x ( - \sin x)}{ (\cos x)^2}\\
\\
\sec ^2 x &= \frac{\cos ^2 x + \sin ^2x}{(\cos x)^2} && \text{Applying the Pythagorean Identity for the trigonometric function } \sin^2x + \cos^2 x = 1\\
\\
\sec ^2 x &= \frac{1}{(\cos x)^2} && \text{Applying the identity } \sec x = \frac{1}{\cos x}\\
\\
\sec ^2 x & = \sec ^2 x

\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}
\text{b.) } \sec x &= \frac{1}{\cos x}\\
\\
\frac{d}{dx} \sec x & = \frac{\cos x \frac{d}{dx} (1) - 1 \frac{d}{dx} \cos x}{(\cos x)^2} && \text{Applying quotient rule}\\
\\
\sec x \tan x & = \frac{0-1 ( - \sin x ) }{(\cos x)^2}\\
\\
\sec x \tan x & = \frac{\sin x}{(\cos x)^2} && \text{Break down two parts}\\
\\
\sec x \tan x & = \frac{\sin x}{\cos x} \cdot \left( \frac{1}{\cos x}\right)\\
\\
\sec x \tan x & = \sec x \tan x
\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}
\text{c.) } \sin x + \cos x &= \frac{1+ \cot x}{\csc x}\\
\\
\frac{d}{dx} \sin x + \frac{d}{dx} \cos x &= \frac{\csc x \frac{d}{dx} (1+\cot x) - (1+\cot x) \frac{d}{dx} \csc x}{(\csc x)^2}\\
\\
\cos x - \sin x &= \frac{\csc x (-\csc^2 x) - ( 1+ \cot x) (-\csc x \cot x)}{(\csc x)^2}\\
\\
\cos x - \sin x &= \frac{-\csc ^3 x + \csc x \cot x + \csc x \cot^2 x}{(\csc x)^2}\\
\\
\cos x - \sin x &= \frac{-\csc^3 x + \csc x \frac{\cos x}{\sin x} + \csc x \frac{\cos^2 x}{\sin ^2 x}}{(\csc x)^2}\\
\\
\cos x - \sin x &= \frac{-\csc^3 x + \csc^2 x \cos x + \csc^3 x \cos x}{(\csc x)^2}\\
\\
\cos x - \sin x &= \frac{\cancel{\csc ^2 x}(- \csc x + \cos x + \cos x \csc x)}{\cancel{(\csc x)^2}}\\
\\
\cos x - \sin x &= \frac{1}{\sin x} + \cos x + \frac{\cos^2 x}{\sin x}\\
\\
\cos x - \sin x &= \frac{\cos ^2 x - 1}{ \sin x} + \cos x && (\cos^x - 1 = -\sin^2 x, \text{ Using Pythagorean Identity})\\
\\
\cos x - \sin x &= - \frac{\sin ^{\cancel{2}}x}{\cancel{\sin x}} + \cos x\\

\end{aligned}
\end{equation}\\
\qquad \boxed{\cos x - \sin x = \cos x - \sin x }
$

Why does Nick tell Gatsby's story in The Great Gatsby?

Arguably, Nick is the narrator of The Great Gatsby because he is an outsider. Nick is not from West or East Egg, for instance, and was, in fact, raised in the Midwest. In addition, Nick does not have the same wealth or status as Gatsby. 
Secondly, Nick is also the narrator of Gatsby's story because he is a non-judgemental type of person, as he admits in the opening chapter:

"I’m inclined to reserve all judgments, a habit that has opened up many curious natures to me."

This makes him the ideal person to tell Gatsby's story because he approaches it with honesty and objectivity. 
Moreover, when Nick finally gets an invitation to one of Gatsby's famous parties, he does not act like the other people there. He actively seeks Gatsby out, for example, and wants to know more about the man himself instead of the persona he has created. 

Nick tells the story of Jay Gatsby because he is arguably the most objective character in the novel. Also, since he has no previous knowledge of Gatsby, Nick can narrate in less of a chronological order than one would expect from those who have been acquainted with him.
As the readers learn about Gatsby in bits and pieces of background mixed with current knowledge, Nick tells readers about Gatsby in non-linear order that is typical of the Modernist movement in literature. In addition, this style of narration also seems more believable because this is the order in which one normally learns about someone. And, for Nick to repeat the fabrications of Jay--such as his war record--lends a trust factor to the narration because he is more naive about Gatsby than others. As he declares, "I am one of the few honest people that I have ever known."
In addition, Nick is a person whom others trust. However, Nick, too, becomes entangled as his own romantic naivete causes him to give more credibility to Gatsby than he would any other character or would an omniscient narrator. Yet, this credibility of Gatsby makes him "great," a man who believes that he can repeat the past and improve upon it.
With the assistance of Nick Carraway as narrator, Gatsby comes alive as a romantic hero. In Chapter Four, Nick narrates,

Then it had not been merely the stars to which he had aspired on that June night. He came alive to me, delivered suddenly from the womb of his purposeless splendor.

But, this romantic hero deteriorates for Nick, and he becomes disillusioned, thinking of returning to the Midwest where he can "run faster" and transcend the past and recreate the past.

College Algebra, Chapter 4, 4.1, Section 4.1, Problem 26

A quadratic function $f(x) = 5x^2 + 30x + 4$.

a.) Find the quadratic function in standard form.


$
\begin{equation}
\begin{aligned}

f(x) =& 5x^2 + 30x + 4
&&
\\
\\
f(x) =& 5 (x^2 + 6x ) + 4
&& \text{Factor out 5 from the $x$-term}
\\
\\
f(x) =& 5 (x^2 + 6x + 9) + 4 - (5)(9)
&& \text{Complete the square: add $9$ inside the parentheses, subtract $(5)(9)$ outside}
\\
\\
f(x) =& 5 (x + 3) - 41
&& \text{Factor and simplify}

\end{aligned}
\end{equation}
$


The standard form is $f(x) = 5 (x + 3) - 41$.

b.) Draw its graph.







c.) Find its maximum or minimum value.

Based from the graph in part (b), since the graph opens upward the minimum value of $f$ is $f(-3) = -41$.

What is Daisy's reaction to Myrtle's death?

Daisy is rattled by the crash but only as it pertains to Daisy. She easily accepts Gatsby's willingness to take the fall and claim he had been driving when it was Daisy driving. This is the turning point, the action, the pattern of Daisy's life--and Tom's too--and epitomizes their marriage and how they approach life. So Daisy's reaction has quickly entailed Tom's. They selfishly move from place to place renewing surface friendships or creating new ones, these relationships relying on their boredom. They are clearly not fulfilled but not searching to be. They amuse themselves with drinking. They roam from place to place making messes for the people around them and move on. Their pattern causes devastation around them. So Daisy slips into the pattern easily after the car crash, dumping Gatsby, turning to Tom as she believes he will fix the situation. They also seemingly get closer, Tom and Daisy. Their now more intense bond about how to get away from what they've caused assures, somewhat, Daisy. Think of the scene where, through a window, we see them sitting at their kitchen table intensely talking about, we assume, their plan to leave, quickly, their current circumstances. In the end, Daisy's reaction is about her concern for herself, not Gatsby, not Myrtle, not the life Tom and Daisy have built, albeit a terribly surface one.

From the description of the accident that Gatsby gives Nick, the reader is meant to infer that she was distraught prior to the accident and after it as well. Shortly after, Fitzgerald paints an entirely different picture; this picture containing Tom and Daisy huddled together not happy nor sad but with conspiring looks. It is clear to the reader that Daisy simply wants to avoid facing the situation, similar to how she deals with any real conflict in the novel. Tom leads George to believe that Gatsby is responsible for Myrtle's death, ultimately leading him to his death. Tom and Daisy ruin the lives of many people in the novel. Without a care in the world, they both disappear to live their comfortably unhappy lives.

Daisy is at first shaken up by Myrtle Wilson's death, which of course she caused—she was driving the car that hit Myrtle outside her house. But beyond her initial reaction, her response to Myrtle's death is to completely wash her hands of it. She allows Gatsby to take the blame for the killing and never acknowledges responsibility herself. This, along with the fact that Tom allows Mr. Wilson to believe that Gatsby was actually having an affair with Myrtle, leads to Gatsby's death. Daisy suffers no visible consequences for Myrtle's death. She goes back to Tom, and together the two of them leave. As Nick says, Daisy, like her husband, is "careless." She, as much as Tom, wrecks the lives of the people she comes across and leaves them to suffer the consequences, "retreating back into their money or their vast carelessness, or whatever it was that kept them together." They destroy the Wilsons as well as Gatsby.

College Algebra, Chapter 9, 9.2, Section 9.2, Problem 60

Suppose an arithmetic sequence has first term $a_1 = 1$ and fourth term $a_4 = 16$. How many terms of this sequence must be added to get 2356?

Using the formula

$a_n = a + (n - 1)d \qquad $ To solve for $d$

$\displaystyle d = \frac{a_n - a}{n - 1} = \frac{a_4 - a_1}{4 - 4} = \frac{16 - 1}{3} = \frac{15}{3} = 5$

We use this to substitute in the formula


$
\begin{equation}
\begin{aligned}

S_n =& \frac{n }{2} [2a + (n-1) d]
\\
\\
2356 =& \frac{n}{2} [2(1) + (n-1)5]
\\
\\
2356 =& \frac{n}{2} (5n -3)
\\
\\
2(2356) =& 5n^2 - 3n
\\
\\
4712 =& 5n^2-3n
\\
\\
0 =& 5n^2 -3n - 4712

\end{aligned}
\end{equation}
$


Using Quadratic Formula,

We have



$
\begin{equation}
\begin{aligned}

n =& \frac{-3 \pm \sqrt{(-3)^2 - 4(5)(-4712)}}{2(5)}
\\
\\
n =& 31 \text{ and } n = \frac{-152}{5}

\end{aligned}
\end{equation}
$


Since $n$ can't have a negative value $n = 31$

It needs $31$ terms in order to get $2356$.

What do Dally and Two Bit want to learn in The Outsiders according to this quote on page 122: "Sixteen years on the street and you can learn a lot. But all the wrong things, not the things you want to learn"?

Thanks! This helped alot

Dally and Two Bit have grown up on the streets. They have learned how to fight, use switchblades, watch for Socs, hide their emotions (especially fear), and trust no one but Greasers.
Dally and Two Bit haven't, however, learned how to live in a non-violent world. They want to learn how to live without fear in a neighborhood without gangs, relate to people, trust, and even love. They want to learn how to hold a respectable job and make a full life for themselves instead of just trying to survive.
As long as they are trapped in the world of gangs and violence, Dally and Two Bit's energy has to be given to surviving, sharpening their skills so they don't get hurt and so they can protect each other. Trust, stability, and a bright future are almost out of reach.

Explain Andrew Jackson’s political philosophy. What were his ideas on the American system of government? How did his ideas compare with those of Alexander Hamilton and the leaders of the American Revolution?

The key to understanding Andrew Jackson's political philosophy is to look back into his life. Jackson was essentially the first common citizen elected into the presidency. He was not born into privilege and suffered many hardships as a child. This directly influenced his later political beliefs. Jackson absolutely favored state's rights and the will of the people. He believed the government's reach should be however long the people of the United States wanted it to be.
The views of Jackson and Hamilton are contrary in one fundamental way: the size of the government. Again, Jackson favored a limited government built on state's rights, while Hamilton saw the need for a strong central government. One element that caught the hatred of Jackson was that of the National Bank. Jackson saw it as corrupt and, worst of all, too powerful. He could not see how the common person benefited from the national bank, while Hamilton viewed it as a vehicle to American infrastructure and expansion.

Andrew Jackson believed in states' rights and in the limits of federal government. This policy ran counter to the ideas of the Whigs and their development of the American system, a plan of economic development that supported a tariff to protect domestic industry, a system of road and canal building, and the founding of the Bank of the United States. Jackson believed that the people should have more direct power in the government, and he supported the expansion of suffrage, or the right to vote. He wanted to make the government more democratic—at least for whites—and he favored the westward expansion of the country.
Jackson's ideas were somewhat similar to those of Thomas Jefferson, who also supported the idea of states' rights. However, Jackson's ideas were in opposition to those of Alexander Hamilton, who supported a strong federal government, the establishment of tariffs, and the foundation of a national bank.

Why does the narrator in "The Cask of Amontlllado" "re-echo" and even "surpass" Fortunato's yelling?

Montresor re-echos and surpasses his victim's desperate cries for help in order to show Fortunato that his cries are useless. By doubling the volume of the noise being made, Montresor demonstrates that the catacombs, deep underground and surrounded by granite, are virtually soundproof. Montresor also gets sadistic pleasure out of adding to Fortunato's torment in this way. He is showing his poor victim that he already thought of everything. The trap is perfect. Fortunato's last hope is futile. Nobody can hear him now, and nobody will be able to hear him after Montresor leaves him to die alone in agony.
This incident also demonstrates to the reader the same thing that is demonstrated to Fortunato. As Montresor explains:

Unsheathing my rapier, I began to grope with it about the recess; but the thought of an instant reassured me. I placed my hand upon the solid fabric of the catacombs, and felt satisfied. I reapproached the wall; I replied to the yells of him who clamoured. I re-echoed, I aided, I surpassed them in volume and in strength. I did this, and the clamourer grew still.

Edgar Allan Poe uses dramatic action and vocal effects to show Montresor chose the ideal location to commit his murder. The nonexistent cask of Amontillado has lured Fortunato into an inescapable death-trap. Poe probably thought it important to show that calling for help would do Fortunato no good, regardless of how long and hard the desperate man screamed and yelled. If the reader thought Fortunato might escape by yelling for help, now or in the future when he was all alone, Montresor effectively disposes of that possibility.